Klopp, speaking at his press conference ahead of Thursday’s Europa League clash with Rubin Kazan, stressed the Reds’ former captain had been in contact, but said Gerrard did not mention returning as a player.

“I spoke with Stevie. One phone call and a few messages. He is a very nice guy I must say,” said Klopp, who has yet to meet Gerrard in person.

“He’s a Liverpool legend, of course, but his contract as I know is in the USA

“But now his break starts and I told him ‘When you are here of course you can come whenever you want, you can train with us if you think it is good for you.

“Of course our doors are always open for him, that is clear. But nothing else.

“Do you think he should play at this moment or next year. No? Why did you ask me?

“Stevie has a contract with LA Galaxy, he loves this club and he is a legend and when his contract has ended we can talk about different stuff.

“We will find for sure something for Stevie when he comes back and whatever he wants to do we will help him but not at this moment – we are in the middle of the season.

“Everything is fine, perfect between LFC and Stevie, but I don’t know him until now and I’m looking forward to the moment we meet each other and we’ll talk about his ideas for the future, maybe, if he has some.

“The door is always open. Of course.”

The midfielder, currently in the Major League Soccer off-season after his summer move to the Los Angeles Galaxy, had initially been offered the opportunity to train at the club’s Melwood base by former boss Brendan Rodgers when the 35-year-old left in May and Klopp is happy to honour that.

Gerrard is set to resume pre-season training in mid-January and his current club have previously played down the chance of a short-term loan, as the likes of David Beckham and Thierry Henry exploited during their time in the United States.

“It could be my last season as a footballer. I certainly don’t want to feel like I’m feeling right now come next year,” he told reporters in America last week.

“I’d love to go out on a high. It’s a long season, and I only came here for the last four months but I’ll certainly be better for the experience next year.”

There does remain a chance, however, he could end up back at Liverpool on the backroom staff in some capacity in the future.

The offer of a contract extension at Anfield was put to Gerrard just under a year ago, but he felt it had come too late and had already started making plans for his next challenge.

However, he subsequently admitted he would have stayed had he been offered a player-coach role to allow him to further his football education.

“What would have kept me at Liverpool into this season was the chance of shadowing Brendan Rodgers and his staff as well as playing – those ideas were only mentioned to me after I had announced I was leaving,” he said in September.

“I could have been a good squad player, a good sub, as well as getting management experience that money can’t buy.”